Complexity theory of real functions
Complexity theory of real functions
Complexity and real computation
Complexity and real computation
On some complexity issues of NC analytic functions
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
| Hi-index | 5.23 |
We discuss the uniform computational complexity of the derivatives of C∞-functions in the model of Ko and Friedman (Ko, Complexity Theory of Real Functions, Birkhäuser, Basel, 1991; Ko, Friedman, Theor. Comput. Sci. 20 (1982) 323-352). We construct a polynomial time computable real function g ∈ C∞ [-1,1] such that the sequence {|g(n)(0)|}n ∈ N is not bounded by any recursive function. On the other hand, we show that if f ∈ C∞ [-1,1] is polynomial time computable and the sequence of the derivatives of f is uniformly polynomially bounded, i.e., |f(n)(x)| is bounded by 2p(n) for all x ∈ [-1,1] for some polynomial p, then the sequence {f(n)}n ∈ N is uniformly polynomial time computable.